12 Chapter Capital Budgeting Slides Developed by: Terry Fegarty Seneca College

1212Chapt

er

Chapt

er Capital BudgetingCapital Budgeting

Slides Developed by:

Terry FegartySeneca College

© 2006 by Nelson, a division of Thomson Canada Limited 2

Chapter 12 – Outline (1)

• Capital Budgeting• Characteristics of Business Projects• Capital Budgeting Techniques

Capital Budgeting Techniques—Payback Capital Budgeting Techniques—Net Present Value

(NPV) Capital Budgeting Techniques—Internal Rate of

Return (IRR) NPV Profile Conflicting Results Between IRR and NPV NPV and IRR Solutions Using Spreadsheets


Chapter 12 – Outline (2)

Projects with a Single Outflow and Regular Inflows Profitability Index (PI) Comparing Projects with Unequal Lives Capital Rationing


Capital Budgeting

• Capital budgeting involves planning and justifying large expenditures on long-term projects

Projects can be classified as:• Replacements• Expansions• New business ventures


Characteristics of Business Projects• Project Types and Risk

Capital projects have increasing risk according to whether they are replacements, expansions or new ventures

• Stand-Alone and Mutually Exclusive Projects A stand-alone project has no competing

alternatives• The project is judged on its own viability

Mutually exclusive projects—when selecting one project excludes selecting the other


Characteristics of Business Projects• Project Cash Flows

First and usually most difficult step in capital budgeting is reducing projects to series of cash flows

Business projects involve early cash outflows and later inflows•Initial outlay is required to get started•Annual net inflows, after tax, generated

by project•Terminal value from sale or salvage of

project


Characteristics of Business Projects• Cost of Capital

Firm’s cost of capital is average rate it pays its investors for use of their money•In general, firm can raise money from two

sources: debt and equity•If potential project is expected to generate

return greater than cost of money to finance it, it is a good investment


Capital Budgeting Techniques

• Four techniques for determining a project’s financial viability: Payback—how many years to recover

project’s initial cost Net Present Value—how much the present

value of project’s inflows exceeds present value of its outflows

Internal Rate of Return—return on investment in the project

Profitability Index—ratio of project’s inflows vs. outflows—in present value terms)


Capital Budgeting Techniques—Payback• Payback period—time to recover early cash

outflows Shorter paybacks are better

• Payback Decision Rules Stand-alone projects

• If payback period < (>) policy maximum accept (reject) Mutually Exclusive Projects

• If PaybackA < PaybackB choose Project A

• Weaknesses of the Payback Method Ignores time value of money Ignores cash flows after the payback period


Capital Budgeting Techniques—Payback—Example

• Consider the following cash flows

Year

0 1 2 3 4

Cash flow (Cn) ($200,000) $60,000 $60,000 $60,000 $60,000

Cumulative cash flows

($200,000) ($140,000) ($80,000) ($20,000) $40,000

Payback period occurs at 3.33 years

Year

0 1 2 3 4

Cash flow (Cn) ($200,000) $60,000 $60,000 $60,000 $60,000

• Payback period is easy to see by the cumulative cash flows

Exa

mpl

e


Example 12.1: Capital Budgeting Techniques—Payback

Q: Use the payback period technique to choose between mutually exclusive projects A and B.

Exa

mpl

e

800200C5

800200C4

350400C3

400400C2

400400C1

($1,200)($1,200)C0

Project BProject A

A: Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4th year. Thus, according to the payback method, Project A is better than B.

Exa

mpl

e


Capital Budgeting Techniques—Payback

• Why Use the Payback Method? Quick and easy to apply Serves as rough screening device

• The Present Value Payback Method Involves finding present value of project’s

cash flows, then calculating project’s payback


Capital Budgeting Techniques—Net Present Value (NPV)• NPV—sum of present values of project’s

cash flows, discounted at cost of capital

If PVinflows > PVoutflows, NPV > 0

1 20 1 2

...(1 ) (1 ) (1 )

nn

CC CNPV C

k k k

PVoutflows

PVinflows


Capital Budgeting Techniques—Net Present Value (NPV)• NPV and Shareholder Wealth

Project’s NPV is net effect that undertaking project is expected to have on firm’s value• A project with NPV > (<) 0 should increase

(decrease) firm value

Since firm desires to maximize shareholder wealth, it should select capital spending program with highest total NPV


Capital Budgeting Techniques—Net Present Value (NPV)

• NPV Decision Rules Stand-alone Projects

• NPV > 0 accept• NPV < 0 reject

Mutually Exclusive Projects• NPVA > NPVB choose Project A over B


Example 12.2: Capital Budgeting Techniques—Net Present Value

Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?

Exa

mpl

e $3,000C3

$2,000C2

$1,000C1

($5,000)C0

A: The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital.

Alpha 1 2 3

1,000 2,000 3,000 -5,000 NPV

1.12 1.12 1.12

-5,000 892.90 1,594.40 2,135.40

-5,000 4,622.70

($377.30)

Since Alpha’s NPV<0, it

should not be undertaken


Example 12.2: Capital Budgeting Techniques—Net Present Value

0 321

-$5,000 $1,000 $2,000 $3,000

Solution is calculated by discount each of the cash flows back to time period zero using a

discount rate of 12%.

$892.90

$1,594.40

$2,135.40

-$377.30Exa

mpl

e


Capital Budgeting Techniques—Internal Rate of Return (IRR)• Project’s IRR is return it generates on

investment of its cash outflows For example, if a project has the following cash flows

0 1 2 3

-5,000 1,000 2,000 3,000

• The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow

The “price” of receiving the inflows


Capital Budgeting Techniques—Internal Rate of Return (IRR)

• Defining IRR Through the NPV Equation The IRR is the interest rate that makes a

project’s NPV zero

outflows

inflows

1 2 n0 1 2 n

C C C: C IRR

1 IRR 1 IRR 1 IRRPV

PV

—


Techniques—Internal Rate of Return • IRR Decision Rules

Stand-alone Projects• If IRR > cost of capital (or k) accept• If IRR < cost of capital (or k) reject

Mutually Exclusive Projects• IRRA > IRRB choose Project A over Project B

• If NPV > 0, IRR > k If NPV < 0, IRR < k


Techniques—Internal Rate of Return

• Calculating IRRs Finding IRRs usually requires an iterative,

trial-and-error technique• Guess at project’s IRR• Calculate project’s NPV using this interest rate

• If NPV is zero, the guessed interest rate is the project’s IRR

• If NPV > (<) 0, try a new, higher (lower) interest rate


Example 12.3: Capital Budgeting Techniques—Internal Rate of Return

Q: Find the IRR for the following series of cash flows:

If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%?

Exa

mpl

e

$1,000

C1

($5,000)

C0

$2,000

C2

$3,000

C3

A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate.

1 2 3

1,000 2,000 3,000 -5,000 NPV

1.12 1.12 1.12

-5,000 892.90 1,594.40 2,135.40

-5,000 4,622.70

($377.30)

Since NPV<0, the project’s IRR must be

< 12%.


Example 12.3: Capital Budgeting Techniques—Internal Rate of Return

A: We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates.

Exa

mpl

e

Since NPV becomes positive somewhere between 8% and 9%, the project’s IRR must be between 8% and 9%. If the

firm’s cost of capital is 8%, the project is marginal. If the

firm’s cost of capital is 9%, the project is not a good idea.

$1307

$228

($83)9

($184)10

($377)12%

Calculated NPV

Interest Rate Guess

The exact IRR can be calculated using a financial calculator or spreadsheet


NPV Profile

• Project’s NPV Profile—graph of its NPV vs. the cost of capital

• It crosses the horizontal axis at the IRR


Figure 12.1: NPV Profile


Techniques—Internal Rate of Return (IRR)• Technical Problems with IRR

Multiple Solutions• If some future cash flows are negative, project

can have more than one IRR solution• Normal pattern involves negative initial outlay and

positive future cash flows• Rarely presents practical difficulties

The Reinvestment Assumption• IRR method assumes cash inflows will be

reinvested at project’s IRR• For projects with extremely high IRRs, this is unlikely


Conflicting Results Between IRR and NPV• NPV and IRR do not always provide the same decision

for a project’s acceptance Occasionally give conflicting results in mutually exclusive

decisions

• If two projects’ NPV profiles cross: one project is accepted below a certain cost of capital the other project is accepted above that cost of capital The NPV profiles have to cross in the first quadrant of the

graph, where interest rates are practical

• NPV method is the preferred over IRR method because the reinvestment interest rate assumption is more practical


Figure 12.2: Projects for Which IRR and NPV Can Give Different Solutions

At a cost of capital of k1, Project A is

better than Project B, while at k2 the opposite is true.


NPV and IRR Solutions Using Spreadsheets • NPV function in Microsoft® Excel®

=Cash Flow0 + NPV(interest rate, Cash Flow1:Cash Flown)

Every cash flow within the parentheses is discounted at the interest rate

• IRR function in Excel®

=IRR (interest rate, Cash Flow0:Cash Flown)


Example 12.3: Spreadsheet Solution E

xam

ple

Formula in B6: =B2 + NPV(C4,C2:E2)

Formula in B8: =IRR(B2:E2,C4)


Projects with a Single Outflow and Regular Inflows• Many projects have one outflow at time 0 and

inflows representing an annuity stream• For example, consider the following cash flows

C0 C1 C2 C3

($5,000) $2,000 $2,000 $2,000

In this case, the NPV formula can be rewritten as

• NPV = -C0 + C[PVFAk, n]

The IRR formula can be rewritten as• 0 = C0 + C[PVFAIRR, n]


Example 12.5: Projects with a Single Outflow and Regular Inflows

Q: Find the NPV and IRR for the following series of cash flows:

Exa

mpl

e

A: Substituting the cash flows into the NPV equation with annuity inflows we have:

NPV = -$5,000 + $2,000[PVFA12, 3]NPV = -$5,000 + $2,000[2.4018] = -$196.40

Substituting the cash flows into the IRR equation with annuity inflows we have:

0 = -$5,000 + $2,000[PVFAIRR, 3]Solving for the factor gives us:

$5,000 $2,000 = [PVFAIRR, 3]

The interest factor is 2.5 which equates to an interest rate between 9% and 10%.

$2,000

C1

($5,000)

C0

$2,000

C2

$2,000

C3


Example 12.5: Spreadsheet SolutionE

xam

ple

Formula in B6: =B2 + NPV(C4,C2:E2)

Formula in B8: =IRR(B2:E2,C4)


Profitability Index (PI)

• Profitability Index—ratio of the present value of a project’s inflows to the present value of a project’s outflows a variation on the NPV method

• Projects are acceptable if PI>1 Larger PIs are preferred



• Also known as the benefit/cost ratio Positive future cash flows are the benefit Negative initial outlay is the cost

1 2 n

1 2 n

0

C C C

1+k 1+k 1+kPI

C

or

present value of inflowsPI

present value of outflows



• PI Decision Rules Stand-alone Projects

• If PI > 1.0 accept• If PI < 1.0 reject

Mutually Exclusive Projects• PIA > PIB choose Project A over Project B

• Comparison with NPV With mutually exclusive projects, two

methods may not lead to same choice


Comparing Projects with Unequal Lives

• If significant difference exists between lives of mutually exclusive projects, direct comparison of the projects is meaningless

• Problem arises due to the NPV method Longer lived projects almost always have

higher NPVs


Figure 12.3: Comparing Projects with Unequal Lives

Exa

mpl

e


Comparing Projects with Unequal Lives—Example

Q:Which of the two following mutually exclusive projects should a firm purchase?

Exa

mpl

e

Short-Lived Project (NPV = $432.82 at an 8% discount rate; IRR = 23.4%)

$750$750$750$750$750$750($2,600)

-

C5

-

C4

$750

C3

Long-Lived Project (NPV = $867.16 at an 8% discount rate; IRR = 18.3%)

$750

C1

($1,500)

C0

$750

C2

-

C6

A: The IRR method favours the Short-Lived Project while the NPV method favours the Long-Lived Project. We’ll correct for the unequal life problem by using the EAA Method.


Comparing Projects with Unequal Lives

• Equivalent Annual Annuity (EAA) Method Replaces each project with an equivalent perpetuity

that equates to the project’s original NPV


Comparing Projects with Unequal Lives—Example

A: The EAA Method equates each project’s original NPV to an equivalent annual annuity.

For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%).

The Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%).

Since the Long-Lived Project has the higher EAA, it should be chosen.

Exa

mpl

e


Figure 12.4: Comparing Projects with Unequal Lives

Exa

mpl

e


Capital Rationing

• Capital rationing— exists when there is limit (maximum) to amount of funds available for new projects

• Thus, there may be some projects with +NPVs, IRRs > discount rate or PIs >1 that will be rejected, because not enough money available

• How do you choose the set of projects in which to invest? Use complex mathematical process called constrained

maximization Use intuition and judgment


Figure 12.5: Capital Rationing

Documents

12 Chapter Capital Budgeting Slides Developed by: Terry Fegarty Seneca College